Abstract

There is a great need for timely prediction of the extent and depth of flooding and related hazards in highly populated urban areas such as the Dallas–Fort Worth metroplex (DFW). The hydrologic, hydraulic and hydrometeorological processes involved and the large number of factors that control them are complex, interrelated and generally scale dependent, which makes real time prediction of flood inundation in urban areas particularly challenging. In addition, a large number of human created structures such as channels, pipes, culverts, buildings, parking lots and manholes add complexity. With continuing urbanization and climate change, it is critical that the dynamics of urban flooding be better understood to improve prediction and to mitigate water related hazards under changing conditions. In this work, we assess how different factors may impact urban flood inundation using the 1D-2D PCSWMM model through a series of controlled simulation experiments. The main study area is the 3.3 km² Forest Park–Berry catchment in Fort Worth in North Central Texas, which has a high density of underground storm drainage. Specifically, we assess the impact of variations in precipitation and impervious cover on simulated inundation maps.

1 Introduction

Urbanization and climate change increase the risks of flooding in many urban areas. According to the Global Health Observatory data of the World Health Organization (WHO 2015), 54% of the global population live in urban areas as of 2014, an increase of 20% from 1960. O’Brien and Burn (2014) and references therein showed evidence of increasing amplitude and decreasing time-to-peak in flooding events as a result of increasing impervious areas. The annual flood loss data for the United States (National Weather Service, NWS, 2015; see Figure 1) indicate that although flood warning has been improving, owing to the increase in both detection and understanding of the causes of heavy-to-extreme precipitation, floods still cause large losses with an annual average in the last 30 y of 89 fatalities and $8.2 billion in damages (Kunkel, Karl, Brooks et al. 2013; Kunkel, Karl, Easterling et al. 2013). Sharif et al. (2014) point out that the annual average number of fatalities in Texas is 16.8 with no apparent downward trend, although a decline may be seen when normalized by population.

Figure 1  Annual (water year) flood damages and fatalities in United States (NWS 2015).

Urban flash flooding, or urban pluvial flooding, is defined as a condition where, as a result of heavy or prolonged rainfall, water escapes from or cannot enter the sewer system or minor urban watercourses, thus remaining on the surface and eventually entering buildings (Ochoa-Rodriguez et al. 2013). The severity of this type of often short term but high peak flooding events depends on many different hydrologic, hydraulic and hydrometeorological factors. The purpose of this work is to assess the different factors that control flood inundation in urban areas using an integrated 1D-2D PCSWMM model through a series of simulation experiments.

2 Study Area

The study area is in Fort Worth in the Dallas–Fort Worth metroplex (DFW) in North Central Texas. According to Zahran et al. (2008), Central Texas is the most flash-flood prone area in North America and DFW is located within Flash Flood Alley. Fort Worth is the sixteenth most populous city in the United States with a population of 777 992 as of 2012 in an area of 904.4 km² that includes parts of Tarrant, Denton and Wise Counties. It has had the highest population growth among large United States cities in the period 2000 to 2013 with a 42.34% increase (Kezar 2014). On the other hand, Walsh et al. (2014) show that the amount of heaviest 1% daily precipitation has increased by 16% in Texas from 1958 to 2012 (Figure 2). Therefore, our study area makes an excellent subject for urban flooding studies under changing conditions.

Figure 2  Increase in daily precipitation in top 1% of the heavy precipitation events in the United States from 1958 to 2012 (Walsh et al. 2014).

The study basin is the Forest Park–Berry catchment (3.28 km², see Figure 3), which drains into the Clear Fork of the Trinity River. The Forest Park–Berry catchment has a long history of flooding (City of Fort Worth 2015). The origin of the flooding problems in the Forest Park–Berry area goes back to the twentieth century when, due to the city’s developing business district, the flood plains of the previously natural water ways were reclaimed and replaced by storm drains of the same capacity which later became inadequate as the development escalated. As a result, despite much effort put in over the years, the area remains flood prone. Figure 4 shows the current storm drainage network in the Forest Park–Berry catchment.

Figure 3 Forest Park–Berry catchment.

Figure 4  Storm drainage network in the Forest Park–Berry catchment.

3 Approach

Table 1 lists the candidate controls considered. In each simulation experiment, the input to the hydrologic and hydraulic models is first specified. Then the hydrologic–hydraulic simulations are made and the corresponding inundation maps are produced.In this study, we focus on precipitation and imperviousness as part of a larger ongoing work. We also compare the performance of the storm drainage network between the current conditions and the altered conditions under continuing urbanization and climate change.

Table 1  Candidate controls in urban flood inundation modeling.

Type	Control
Hydrometeorological	Magnitude of precipitation Spatiotemporal variability of precipitation (Effective) Resolution of precipitation input
Hydrologic	Topography, resolution of Digital Elevation Model (DEM) Resolution of subcatchment delineation Imperviousness, land use Initial soil moisture
Hydraulic	Roughness coefficient Slope, size, and length of storm drains Initial conditions Mesh size

4 Models Used

Despite recent advances in computing, data science and technology, and remote sensing, which led to the emergence of new models for urban flooding (Chang et al 2015; Gires et al. 2014), high resolution urban inundation mapping is still a relatively new area of research. Different approaches exist for modeling urban pluvial flooding (van Dijk et al. 2014). Zhang and Pan (2014) compared some of the most commonly used models in terms of hydrologic and hydraulic modules, model input and output, and applicable flood types. Among them, dual drainage 1D-2D models have been gaining popularity for simulating urban flooding in recent years, due to their computational efficiency compared to full 2D models (Nania et al. 2014).

Two types of overland flow occur in urban flooding (Ochoa-Rodriguez et al. 2013):

• direct runoff following abstraction which then enters the storm drainage network (runoff concentration); and
• surcharged runoff from exceeding the storm drainage network’s capacity which then joins overland flow (exceedance overland flow).

The first is simulated with hydrologic models and the second with hydraulic models. In this study, we used the integrated 1D-2D PCSWMM model which combines a semi-distributed hydrologic routing model, a 1D hydraulic model for the storm drainage network, and a 2D overland flow model. PCSWMM uses the Storm Water Management Model Version 5 (Rossman 2010) engine for modeling junctions, or nodes, and conduits, or links, of various cross sections and connects them to a 2D overland flow model for 1D-2D dual drainage modeling. PCSWMM also has the capability to ingest radar based quantitative precipitation estimates (QPE). The choice for the coupled hydrologic–hydraulic modeling approach is based on the need to account for both types of flow in the study basins.

To set up the integrated 1D-2D PCSWMM model, we followed the steps in Figure 5. The subcatchments were delineated by inputting the digital elevation model (DEM) into the Arc Hydro GIS tool (Maidment 2002), and locating outlets and identifying the contributing areas (see Figure 6).

Figure 5  Steps used in hydrologic–hydraulic modeling.

Figure 6  Elevation map and subcatchment delineation.

Precipitation is the main forcing for flooding. Spatiotemporal variability of precipitation and the accuracy and resolution of QPE are among the most influential factors in inundation mapping particularly for small and highly impervious urban catchments. Ochoa-Rodriguez et al. (2013) summarize the results of a number of studies to conclude that for detailed urban hydraulic modeling, rainfall forcing should have a spatiotemporal resolution higher than 100 m to 500 m and 1 min to 5 min.

In this study, we used the 1 min–500 m resolution QPE from the Collaborative Adaptive Sensing of the Atmosphere (CASA) X-band weather radar located at the University of Texas at Arlington (UTA). The radar XUTA is one of seven X-band radars currently in operation in the DFW Demonstration Network (Habibi et al. 2016).

A severe flash flooding occurred in the area on 2014-06-24. During this event, >70 mm of rain fell in just a few hours (see Figures 7 and 8) resulting in severe inundation in some areas of the city, which resulted in >40 responses from the Fort Worth emergency services (FloodList 2014).

Figure 7  NEXRAD QPE for the 2014-06-24, event (1 in. = 25.4 mm).

Figure 8  The XUTA-observed rainfall map for 2014-06-24.

Using PCSWMM’s Radar Acquisition and Processing (RAP) tool, the hyetographs were produced for all subcatchments from the CASA QPE for 2014-06-24. The reader is referred to Habibi et al. (2016) for the CASA QPE generation process. Figure 8 shows the 24 h rainfall map as estimated from XUTA. The black lines in the figure delineate, from left to right, the cities of Fort Worth, Arlington, Grand Prairie, and parts of Dallas. The hyetographs derived above represent the baseline input in the reference scenario. The input is then modified by ±15% for sensitivity analysis. Three example hyetographs derived from the CASA QPE are shown in Figure 9.

Figure 9 Three examples of derived hyetographs for the 2014-06-24, event (the solid red line is for a downstream subcatchment; the dashed black line is for a subcatchment in the centre of the study area; and the dashed blue line is for a subcatchment in upstream part of the study area).

To model the mean areal impervious fraction for each subcatchment, an impervious cover map was used consisting of a building footprint layer, parking lots and streets (Figure 10).

Figure 10 Mean areal impervious fraction for each subcatchment.

For 2D overland flow modeling, the building footprint layer, representing obstructions, was added. Other model parameters were specified, wherever possible, based on the information available from the City of Fort Worth as explained below. The elevations of most inlets and pipes were available. Missing elevations were handled differently case by case depending on the location. If the elevation of an inlet node was not available, the overlain ground surface elevation from the DEM was used. If the underground elevation was missing, a distance based interpolation technique was used to estimate the elevation from the known neighbouring elevations. Since PCSWMM does not allow variable Manning roughness values in a 2D mesh boundary, we used a constant Manning roughness of 0.015 for all 2D cells.The flow length parameter for each subcatchment was estimated based on the flow accumulation map. For runoff generation, the SCS curve number (CN) method was used (Chow et al. 1988). The spatially varying CNs were initially extracted from the hydrologic models provided by the City of Fort Worth. However, a sensitivity analysis showed little difference in inundation maps due to spatially varying CN vs spatially uniform CN for heavy-to-extreme rainfall cases. Therefore, the average CN of 80 was used in the simulations. Surface storage was neglected, given that they will be quickly filled in the very-heavy-to-extreme rainfall events modeled here. Table 2 summarizes the model parameters.

Table 2  Model parameters.

Parameter	Description
Infiltration method	SCS curve number
Flow routing method	Dynamic wave (Rossman 2010)
Manning roughness of the pipes	0.013
Manning roughness of 2D mesh	0.05
Manning roughness of impervious surfaces	0.012
Manning roughness of pervious surfaces	0.015
2D domain area	1.67 x 107 ft2 (~1.55 x 106 m2)
2D mesh type	Hexagonal
2D mesh resolution	35 ft (~10.67 m)
Number of cells	14 268

Figure 11 shows a part of the integrated model and an example inundation result.

Figure 11  Part of the 1D-2D integrated model domain and an example of simulated inundation.

In the initial stages of the simulation study, the impact of the resolution of subcatchment delineation on runoff was analysed using a 1D model. A large impact was seen. The effect of spatial resolution of subcatchment delineation on hydrologic simulation has been extensively studied. The state of the art review of urban hydrological modeling in Salvadore et al. (2015) concludes that high spatial resolution is required for resolving the heterogeneity and fast dynamics of urban hydrological processes. Ghosh and Hellweger (2011), who investigated the scale effect using SWMM, concluded that coarser subcatchment delineations undersimulate the peak flows in large storms. Note that the SWMM engine uses semi-distributed modeling and, by construction, runoff from each subcatchment has only a single point of entry into either a junction or a downstream subcatchment. If the subcatchment is so large that it contains multiple inlets, they are ignored except the one identified as the outlet. If, on the other hand, the subcatchment is excessively small, the connectivity of the subcatchments may not be physically realistic due to possible errors in the DEM and storm drain data. Note also that subcatchment delineation is impacted also by the resolution of the DEM used. Lastly, it is very difficult in SWMM based modeling to break up channels into multiple sections because short conduits can potentially cause numerical instabilities. Therefore, the approach taken in this study was to produce the finest subcatchments that may be derived using the available 5 m resolution DEM and the inlet locations. The delineated subcatchments were then visually inspected to identify any clearly erroneous or suspect results. It was found that the erroneous delineations were due to the high resolution of the DEM which resulted in unrealistically small subcatchments at a few locations.

6 Simulation Experiments, Results and Discussion

The main focus of the study was to assess the impact of variations in precipitation magnitude and the percentage of impervious cover. They are directly associated with climate change and urbanization and hence are of particular interest. We used the 2014-06-24, flash flooding event and the imperviousness percentage map in Figure 10 as references, and perturbed the precipitation magnitude and imperviousness as summarized in Table 3 to produce a total of nine different simulations. Wobus et al. (2015) used 3 different climate models to project changes in heavy-to-extreme precipitation. While consistent patterns were not found in the model projections of heavy-to-extreme precipitation, they report approximately a 15% change in precipitation amount for the study area. This figure is also comparable to the 16% change in observed precipitation for large amounts for our study area (Figure 2). As such, we chose 15% for the sensitivity analysis.

Table 3  List of model simulations.

		Impervious Cover
		-15%	Existing	+15%
Precipitation	-15%	Case 1	Case 2	Case 3
	Base	Case 4	Case 5	Case 6
	+15%	Case 7	Case 8	Case 9

The impact of the changes in precipitation amounts and imperviousness was assessed by comparing the extent and depth of inundation and flow velocity. Figure 12 shows the extent of inundation, as measured by the number of wet cells at each time step, for the nine different cases. For all cases, the maximum inundation extent increases sharply in the first 20 min, less so from 20 min to 30 min and very slowly after 30 min. It is interesting to note that the maximum difference among the 9 cases occurs at ~12 min when the inundation extent is fast increasing. The difference is ~10% of the total inundation extent. It suggests that changes in precipitation amount and imperviousness may significantly alter the wetting dynamics even though the final inundation extent may be similar (see the results at 60 min).

Figure 12  Simulated inundation extent as a function of time elapsed.

The differences among the nine cases are more discernible in location specific analyses. Figure 13 shows the maximum inundation depth for the 9 cases. Comparison of cases 1 through 9 shows that, the modeled inundation is more sensitive to a 15% change in precipitation than to change in imperviousness.

Figure 13  Spatial comparison of maximum inundation depth; the columns have been multiplied by a factor of 300 for better discernibility.

Figure 14 shows the relative magnitude of standard deviation of maximum inundation depths among the 9 cases. It is seen that, although the variation of inundation is generally higher in the downstream parts of the study area, there exist some interior locations with very large variations. Since they are all located along the storm drainage network depicted by red lines in the figure, one may hypothesize that the large variations are due to the limited capacity of the pipes. For example, when a certain pipe is not at full capacity in some cases but becomes surcharged in other cases, one may expect large variations in inundation depth at its inlet cell. In fact, using PCSWMM’s design tool, it was found that almost 40% of the pipes become surcharged for the 2014-06-24 extreme event.

Figure 14  Relative magnitude of standard deviation of maximum inundation depth. The columns have been multiplied by a factor of 3 000, for better discernibility.

Figures 15 and 16 show the time series of the location-specific depth and velocity, respectively, for the 2D cell encircled in red in the inset of Figure 15.

Figure 15  Location specific comparison of simulated depth time series.

Figures 15 and 16 show an increasing trend in peak inundation depth and velocity respectively, with increasing impervious cover and increasing precipitation. The maximum difference in peak depth is about 17% which occurs between case 1 and case 9. The figures also show that increased rainfall increases peak discharge more so than increased impervious cover. In addition, the effect of imperviousness decreases when precipitation is more intense.

Figure 16  Location specific comparison of simulated velocity time series.

The patterns in the velocity time series in Figure 16 are generally similar to those of peak inundation depth. Note, however, that at about 10 min into the event the velocity is reduced to near zero though the depth is non-zero, an indication that ponding may be occurring, due possibly to an overwhelmed drainage system before flow resumes. Similar analysis may be performed for different locations of interest. One may also delineate the areas of increased risks by identifying all locations where the maximum depth or velocity exceeds some critical threshold.

 While useful, the type of local analyses shown above is not very practical when many locations are involved. Therefore there is a need for more general, model domain-wide comparisons and characterization of the simulation results. To that end, we derived the empirical cumulative distribution functions (ECDF) of the simulated inundation duration, depth, and velocity (see Figures 17 to 19). The figures consider only the wet cells; all cells that remained dry during the event were excluded. Also, because we are interested primarily in higher depths and velocities, only the upper tails are shown in Figures 18 and 19.

Figure 17  ECDFs of simulated inundation duration.

Figure 18  ECDFs of simulated maximum inundation depth.

Figure 19  ECDFs of simulated maximum flow velocities.

Figure 17 indicates that, for example, given that some location gets inundated at all during the 60 min event, there is ~58% chance the inundation lasts for ≥50 min. Similarly, the chances of inundation at the location lasting >20 min, >30 min and >40 min are ~97%, ~92% and ~80%, respectively. Figure 17 indicates that the variations in the inundation duration among the 9 cases can be as large as 7 min (at the exceedance probability of 0.95). It can also be seen in Figure 17 that the exceedance probability of occurrence of the same inundation duration can vary up to 7%, which occurs at 46 min, among the 9 cases.

Figure 18 shows that, for example, the probability of maximum inundation depth >20 cm at some location that gets inundated at all during the 60 min event is ~1%. This probability increases by ~0.5% from case 1 to case 9. Similarly, the probability of maximum inundation depth >40 cm varies from ~0.4% to ~0.7% for cases 1 through 9. Note that these variations in exceedance probabilities are large, with potentially very significant implications in hydrologic design in urban areas.

Figure 19 is completely analogous to Figure 18 but it is for maximum flow velocity. Figure 19 indicates that the probability of maximum velocity >0.8 m/s at some location that gets inundated at all during the 60 min event increases from ~0.2% in case 1 to ~0.8% in case 9. For velocities >0.5 m/s, the probabilities vary from ~1.6% in case 1 to ~2.7% in case 9.

Verification of the model simulation results was carried out qualitatively by comparing with the locations of historical high water reports. The simulated inundation extent for the 2014-06-24 rainfall event used for our simulation experiments matched reasonably well with the high water reports. Of the seven reports in our study area, four matched with the PCSWMM modeled inundation areas, two were approximately a block away from the nearest simulated wet cell, and one was missed by a large margin. Due to lack of permission to publish the above reports, in this paper we present the high water reports from a larger event of 2009-10-21, which produced 5.5 in. to 6 in.(14.0 cm to 15.2 cm) rainfall in a 24 h period (see Figure 20). Though the model simulation is not for the same event, one may expect a simulated inundation extent similar to the 2014-06-24 case owing to the fact that this is very small catchment (3.3 km²) and hence spatial variability of rainfall is not very important. Among the six available high water records for this heavier rainfall event, four are within the modeled inundation extent. The model simulation, however, missed two high water locations in the eastern part of the catchment. This is likely due to the fact that the 2009-10-21 event was more intense and hence flooding was probably more severe than indicated by the 2014-06-24 simulation.

Figure 20 Comparison of 2014-06-24 model simulation with historical high-water reports. (Disclaimer: flooding incidence data provided by the City of Fort Worth for informational purposes only; the City of Fort Worth assumes no responsibilities for the accuracy of the data.)

As illustrated above, lack of observations poses a large challenge in verification of inundation mapping which requires spatially dense and frequently sampled ground truths. We note here that we are deploying real time water level sensors in the study area and elsewhere in the DFW area and will be gathering crowdsourced observations for near real time and post event verification (Hanna 2016).

7 Conclusions and future research recommendations

This work assesses the impact of variations in hydrologic, hydraulic and hydrometeorological factors that control urban inundation. The study area is a flooding prone urban catchment in Fort Worth in North Central Texas. This study was focused on the assessment of changes in precipitation magnitude and imperviousness. The results of the nine simulation experiments presented in this work highlight the large impact of changes in precipitation and impervious cover on local and catchment scale urban flooding. They suggest that, with climate change and continuing urbanization, for accurate mapping of inundation in urban areas, high resolution rainfall forcing and physiographic information are essential.

Once demonstrated operation-worthy, we plan to run the integrated 1D-2D model in real time for selected urban catchments in the DFW area as a part of the flash flood warning system under implementation for the area (Habibi et al. 2016). The sensitivity analyses undertaken in this work are part of the effort to assess the feasibility of real time operation of a 1D-2D model, to identify potential alternatives for reduced complexity and computational requirements, to increase lead time by the use of rainfall nowcasts (Ruzanski et al 2011; Ruzanski and Chandrasekar 2012) and to develop impact based warning products (Calianno et al 2013).

Due to a sparsity of observations, verification of high resolution prediction is a large challenge. While the model results are generally in agreement with historical reports of inundation (Nazari et al. 2014), they are yet to be verified dynamically. For that, we will be using observations from a network of recently deployed real time water level sensors and the newly developed crowdsourcing app, iSeeFlood. Higher resolution modeling does not always result in higher accuracy while potentially imparting a false sense of confidence in high resolution output (Dottori et al. 2013). To provide a measure of uncertainty associated with inundation mapping, ensemble approaches (Aronica et al. 2012, Gires et al. 2014) or other probabilistic methods (Fu et al. 2011) are necessary. To that end, we plan to explore ensemble inundation mapping as a part of the ongoing effort on integrative sensing and prediction of urban water for sustainable cities (Seo et al. 2015).

8 Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No. IIP-1237767 (Brenda Philips, Unversity of Massachusetts Amherst, Principal Investigator, PI) and CyberSEES-1442735 (Dong-Jun Seo, University of Texas at Arlington, PI), and by the City of Fort Worth. These supports are gratefully acknowledged.

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